Question

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Part 1
A car rental agency charges ​$27 per day to rent a car and ​$12.95 per day for a global positioning system​ (GPS). Customers are charged for their full tank of gas at ​$3.80 per gallon. A car has a 11 gallon tank and a GPS.
​a) Write a function rule for the total bill b as a function of the days d the car is rented.
​b) What is the bill for a 10 day​ rental?
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Part 1
​a) Choose the correct function rule for the total bill b as a function of the days d the car is rented.
​(Type an integer or a​ decimal.)
A.
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B.
dequals
  
enter your response herebplus
  
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C.
bequals
  
enter your response heredplus
  
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D.
bequals
  
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Answer 1

What is the bill for a 10 day​ rental?
​$
  
enter your response here

Answer 2

To write a function rule for the total bill \( b \) as a function of the number of days \( d \) the car is rented, we need to consider each component of the cost:

1. **Car rental cost per day**: $27 per day
2. **GPS rental cost per day**: $12.95 per day
3. **Gas cost**: The car has a 11-gallon tank, and if you fill it up, it costs $3.80 per gallon.

First, we can calculate the gas cost:
\[
\text{Gas cost} = \text{Price per gallon} \times \text{Gallons} = 3.80 \times 11 = 41.80
\]
Now, we can find the total daily rental cost:
\[
\text{Total daily rental cost} = \text{Cost of car rental per day} + \text{Cost of GPS per day} = 27 + 12.95 = 39.95
\]

Now, the total bill \( b \) can be expressed as:
\[
b = (\text{Total daily rental cost} \times d) + (\text{Gas cost})
\]
Substituting the values:
\[
b = (39.95 \times d) + 41.80
\]

### Part 1: Function Rule
So the function rule for the total bill \( b \) as a function of the days \( d \) the car is rented is:
\[
b = 39.95d + 41.80
\]

### Part 2: Bill for a 10-day Rental
To find the bill for a 10-day rental, substitute \( d = 10 \):
\[
b = 39.95 \times 10 + 41.80
\]
Calculating this gives:
\[
b = 399.50 + 41.80 = 441.30
\]

### Final Answers:
a) The function rule is:
\[
b = 39.95d + 41.80
\]

b) The bill for a 10-day rental is:
\[
b = 441.30
\]

Answer 3

To calculate the bill for a 10-day rental using the function we derived earlier, we substitute \( d = 10 \) into the function:

\[
b = 39.95d + 41.80
\]

Substituting \( d = 10 \):
\[
b = 39.95 \times 10 + 41.80
\]
Calculating that:
\[
b = 399.50 + 41.80 = 441.30
\]

Therefore, the bill for a 10-day rental is:
\[
\text{Bill} = \boxed{441.30}
\]

So you would enter:
\[
\text{\$441.30}
\]